(12) 4931/(Set : B) खण्ड-स SECTION-C 12. समीकरण tamH-tany को हल कीजिए। Salve the equation tan 'EE-Ptan's

निम्न समीकरण को हल कीजिए - tan^(-1)(x-1)+tan^(-1)(x)+tan^(-1)(x+1)=tan^(-1) 3 x

Let tan ^(-1)2x+tan^(-1)3x=(pi)/(4) where x>=0 Let S is the set containing all the solutions of the equation then S contains (A) one element (B) Two element (C) more than two element (D) none of these

If ABCD is a cyclic quadrilateral such that 12 tan A-5=0 and 5cos B+3=0 then the quadratic equation whose roots are cos C and tan D is

A long string having a cross- sectional area 0.80 mm^2 and density 12.5 g cm^(-3) is subjected to a tension of 64 N along the X-axis. One end of this string is attached to a vibrator moving in transverse direction at a frequency fo 20Hz. At t = 0. the source is at a maximujm displacement y= 1.0 cm. (a) Write the equation for the wave. (b) What is the displacement of the particle of the string at x = 50 cm at time t = 0.05 s ? (c) What is the velocity of this particle at this instant ?

A long string having a cross- sectional area 0.80 mm^2 and density 12.5 g cm^(-3) is subjected to a tension of 64 N along the X-axis. One end of this string is attached to a vibrator moving in transverse direction at a frequency fo 20Hz. At t = 0. the source is at a maximujm displacement y= 1.0 cm. (a) Write the equation for the wave. (b) What is the displacement of the particle of the string at x = 50 cm at time t = 0.05 s ? (c) What is the velocity of this particle at this instant ?

If tan((pi)/(12)) is one of the rootsofthe equation 2x^(2)-bx+c=0,(b,c in Q) then (b+c)=

Consider the quadratic equation (c - 5)x^(2) - 2cx + (c - 4) = 0, c ne 5 . Let S be the set of all integral values of c for which one root of the equation lies in the interval (0, 2) and its other root lies in the interval (2, 3). Then the number of elements in S is a. 11 b. 18 c. 10 d. 12

Consider the quadratic equation (c - 5)x^(2) - 2cx + (c - 4) = 0, c ne 5 . Let S be the set of all integral values of c for which one root of the equation lies in the interval (0, 2) and its other root lies in the interval (2, 3). Then the number of elements in S is a. 11 b. 18 c. 10 d. 12

The smallest value of theta satisfying the equation sqrt(3)(cot theta+tan theta)=4 is 2 pi/3 b.pi/3c. pi/6d. pi/12